Magnetic Circuits
EE 340
Spring 2013
Ampere’s Law
• Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
where H is the magnetic field intensity
• At a distance r from the wire,
IdlH.
IrHdlH )2.(.
Magnetic Flux Density
• Relation between magnetic field intensity H and magnetic field density B:
where is μr is the relative permeability of the medium (unit-less), is μo is the permeability of free space (4πx10-7 H/m)
HHB r )( 0
B-H Curve in air and non-ferromagnetic material
B-H Curve in 3 Ferromagnetic materials
Saturation curves of magnetic and nonmagnetic materials
Residual induction and Coercive Force
Hysteresis Loop (AC Current)
Ampere’s Law applied to a magnetic circuit (Solid Core)
• Magnetic flux (Wb):
• Hence,
NIlB
HldlH
.
BAdsB
)(A
lNI
Analogy between electric and magnetic circuits
Ampere’s Law applied to a magnetic circuit (core with air gap)
NI
NIlB
lB
lHlHdlH a
o
c
or
aacc.
A
l
A
l
o
a
or
c
where
Faraday’s Law
• Faraday's law of induction is a basic law of electromagnetism relating to the operating principles of transformers, inductors, electrical motors and generators. The law states that:
“The induced electromotive force (EMF) in any closed circuit is proportional to the time rate of change of the magnetic flux through the circuit”
Or alternatively, “the EMF generated is proportional to the rate of change of the magnetic flux”.
dt
dNe
Voltage induced in a coil when it links a variable flux in the form of a sinusoid
Example: voltage induced in a coil by a moving magnet
E = -NΔφ/Δt= -2000(-3/0.1)=60,000 mV or 60 V
Inductance of a coil
l
ANL
dt
dilAN
dt
lANidN
dt
dN
dt
diLe
22 )/(
)/(
Induced Force on a Current Carrying Conductor
Problems (Chap. 1)
• 5, 6, 8, 10, 12, 14